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Researchers often have difficulties collecting enough data to test their hypotheses, either because target groups are small or hard to access, or because data collection entails prohibitive costs. Such obstacles may result in data sets that are too small for the complexity of the statistical model needed to answer the research question. This uniquebook provides guidelines and tools for implementing solutions to issues that arise in small sample research. Each chapterillustrates statistical methods that allow researchers to apply the optimal statistical model for their research question when the sample is too small. Thisessential book will enable social and behavioral science researchers to test their hypotheses even when the statistical model required for answering their research question is too complex for the sample sizes they can collect.The statistical models in the book rangefrom the estimation of a population mean to models with latent variables and nested observations, and solutions include both classical and Bayesian methods.All proposed solutions are described in steps researchers can implement with their own data and are accompanied with annotated syntax in R. The methods described in this book will be useful for researchers across the social and behavioral sciences, ranging from medical sciences and epidemiology to psychology, marketing, and economics.

"Meuleman and Billiet (2009) have carried out a simulation study aimed at the question how many countries are needed for accurate multilevel SEM estimation in comparative studies. The authors concluded that a sample of 50 to 100 countries is needed for accurate estimation. Recently, Bayesian estimation methods have been introduced in structural equation modeling which should work well with much lower sample sizes. The current study reanalyzes the simulation of Meuleman and Billiet using Bayesian estimation to find the lowest number of countries needed when conducting multilevel SEM. The main result of our simulations is that a sample of about 20 countries is sufficient for accurate Bayesian estimation, which makes multilevel SEM practicable for the number of countries commonly available in large scale comparative surveys." (author's abstract)

Nationwide opinions and international attitudes toward climate and environmental change are receiving increasing attention in both scientific and political communities. An often used way to measure these attitudes is by large-scale social surveys. However, the assumption for a valid country comparison, measurement invariance, is often not met, especially when a large number of countries are being compared. This makes a ranking of countries by the mean of a latent variable potentially unstable, and may lead to untrustworthy conclusions. Recently, more liberal approaches to assessing measurement invariance have been proposed, such as the alignment method in combination with Bayesian approximate measurement invariance. However, the effect of prior variances on the assessment procedure and substantive conclusions is often not well understood. In this article, we tested for measurement invariance of the latent variable "willingness to sacrifice for the environment" using Maximum Likelihood Multigroup Confirmatory Factor Analysis and Bayesian approximate measurement invariance, both with and without alignment optimization. For the Bayesian models, we used multiple priors to assess the impact on the rank order stability of countries. The results are visualized in such a way that the effect of different prior variances and models on group means and rankings becomes clear. We show that even when models appear to be a good fit to the data, there might still be an unwanted impact on the rank ordering of countries. From the results, we can conclude that people in Switzerland and South Korea are most motivated to sacrifice for the environment, while people in Latvia are less motivated to sacrifice for the environment.